Wierd shading when cutting faces
Shading issues most commonly occur because of the presence of non-quad geometry (especially near edges).

As can be seen in your picture, the "quads" surrounding your highlighted section have more than 4 vertices apiece. This is as a result of your use of the knife tool. There are a myriad of methods you can employ to "correct" the geometry (often this involves moving unavoidable n-gons to flat sections to avoid shading issues), but could also involve simply extending the new edges all the way around the mesh - it all depends on how "clean" and "orderly" you need the final mesh to be.

A second reason for shading issues (and what seems to also be the case here) is a case of supporting geometry. Generally, supporting geometry is used to sharpen the appearance of edges,however, it can have the side effect of causing "ugly creases" to appear (especially on curved surfaces) when there is uneven spacing between edges or edge loops. If two edges on a curved surface are too close together, they will highlight the "crease" between two flat faces that are being shaded to appear smooth.

I suggest you spend a bit of time practicing some simple topology exercises, just to get a feel for the "rules" so to speak, as well as what you can and can't get away with without causing shading issues.

Best of luck.